Banding device (4) for encircling an object which has a cross-section having a regular-shaped perimeter, said device comprising a band (5) with a clamping strip (6) which forms a loop intended to surround the object, the clamping strip (6) comprising a central portion (9) which has a shape substantially corresponding to the shape of the perimeter of the cross-section of the object and two strands (7, 8) comprising the respective ends (10, 11) of the clamping strip, the shape of which departs from the shape of the perimeter of the cross-section of the object, the band comprising at least one so-called central runner (16) which is mounted on at least one of the strands (7; 8) in such a way as to be interposed between the object (101) and the strand (7; 8).